As technology has advanced, cameras have advanced accordingly but still face certain persistent issues. Particularly, as light passes through a camera lens, the light is bent as the light refracts. This bending of light results in inconsistent brightness across the sensor such that areas in the middle are much brighter than areas on the edges. This distortion is known as lens shading or vignetting. Variations or imperfections in the lens have an increasing impact on the inconsistency of light coming out of the lens. Further, light may get stuck or not pass through as a result of interacting with the lens housing. Thus, light coming through a lens system and forming an image on a film plane (digital sensor or film) will be unevenly attenuated across the image plane and color spectrum due to imperfections in the lens and image forming medium (film or digital array of sensors). The overall result is that if a “flat” field of light enters the lens, then the film or digital sensor nevertheless receives an “unflat” field of light with varying brightness.
Conventionally, a high order polynomial may be used to represent this distortion and can be applied across the image plane to attempt to overcome the impact of lens shading and lens imperfections thereby correcting the image. However, the high order polynomials are computationally expensive and are complicated to execute on hardware of fixed precision. For example, a 10th power polynomial may have 100 individual terms and a high order polynomial may require evaluation at each pixel meaning that, for instance, after 20 pixels, the amount of computations required increases rapidly. Further, higher order polynomials are numerically unstable as small variations can result in large changes in the polynomial. Also, as one moves around a surface defined by a polynomial to the 9th or 10th order, the polynomial coefficients provide little intuition as to the magnitude of the changes in the surface value in any direction. All these characteristics make polynomial representation not a viable solution for the lens shading problem in terms of being computationally intensive and not intuitive.